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1、1Whatismathematics?Forallthetimeschoolsdevotetotheteachingofmathematics,verylittle(ifany)isspenttryingtoconveyjustwhatthesubjectisabout.Instead,thefocusisonlearningandapplyingvariousprocedurestosolvemathproblems.That’sabitlikeexplainingsoccerbysayingitisexecutingaseriesofmaneuverstogettheball
2、intothegoal.Bothaccuratelydescribevariouskeyfeatures,buttheymissthewhatandthewhyofthebigpicture.Giventhedemandsofthecurriculum,Icanunderstandhowthishappens,butIthinkitisamistake.Particularlyintoday’sworld,ageneralunderstandingofthenature,extent,power,andlimitationsofmathematicsisvaluabletoany
3、citizen.1 Overtheyears,I’vemetmanypeoplewhograduatedwithdegreesinsuchmathematicallyrichsubjectsasengineering,physics,computerscience,andevenmathematicsitself,whohavetoldmethattheywentthroughtheirentireschoolandcollege-leveleducationwithoutevergainingagoodoverviewofwhatconstitutesmodernmathema
4、tics.Onlylaterinlifedotheysometimescatchaglimpseofthetruenatureofthesubjectandcometoappreciateitspervasiveroleinmodernlife.21.1 MorethanarithmeticMostofthemathematicsusedinpresent-dayscienceandengineeringisnomorethanthree-orfour-hundredyearsold,muchofitlessthanacenturyold.Yetthetypicalhigh
5、schoolcurriculumcomprisesmathematicsatleastthatold—someofitovertwo-thousandyearsold!Now,thereisnothingwrongwithteachingsomethingsoold.Asthesayinggoes,ifitain’tbroke,don’tfixit.ThealgebrathattheArabic-speakingtradersdevelopedintheeighthandninthcenturies(theword algebra comesfromtheArabicterm a
6、l-jabr, meaning“restoration”or“reunionofbrokenparts”)toincreaseefficiencyintheirbusinesstransactionsremainsasusefulandimportanttodayasitwasthen,eventhoughtodaywemaynowimplementitinaspreadsheetmacroratherthanbymedievalfingercalculation.Buttimemovesonandsocietyadvances.Inthe process,theneedforn
7、ewmathematicsarisesand,induecourse,ismet.Educationneedstokeeppace.Mathematicscanbesaidtohavebegunwiththeinventionofnumbersandarithmetic,whichisbelievedtohaveoccurredaroundtenthousandyearsago,withtheintroductionofmoney.(Yes,apparentlyitbeganwi
